1. Field of the Invention
The present invention relates to an analyzer of time series data such as electroencephalogram data and a computer-readable recording medium recording a time series data analysis program.
2. Description of the Related Art
The present inventor found that with regard to the chaotic time series following the respective nonlinear motion equations of Lorenz, Roessler and Duffing Models, all the spectra of the time series are exponential spectra, and reported the finding on a journal written in English of The Physical Society of Japan (Document 1) in 1995. The Japanese version of Document 1 is published in Document 2 in 1996.
In addition, the inventor analyzed, in the Document 1, the pulse wave (blood pressure waveform) data of one beat by the same method, and found that the spectrum of the data is an exponential spectrum, indicating the relation of physiological phenomena with chaotic characteristics. The Document 1 triggered the wide attention paid to the exponential spectra in the relation between chaotic time series and physiological phenomena, etc.
The Document 1 presents the important findings obtained for the first time by precisely calculating the spectra of chaotic time series using a highly precise general-purpose time series data analysis system, MemCalc (registered trademark) prepared by the present inventor. Thereafter, with the widespread use of the MemCalc (registered trademark) and application systems thereof, the group including the present inventor, and also many other researchers and groups have studied the features of spectra of various time series data, particularly biological time series data in detail.
In this situation, above all, the electroencephalogram data and analysis results thereof described in Document 3 are very interesting. The facts revealed by the Document 3 include that the spectrum of the electroencephalogram data measured at the scalp is an exponential spectrum in the frequency band of interest (1 to 30 Hz or 0.5 to 30 Hz), that the overall trend of the spectrum varies depending on the age and state of the subject, that the overall trend of an electroencephalogram spectrum varies in response to “the rhythm of sleep” about every one hour and a half also during sleep, and that the introduction of anesthesia also changes the overall trend of the spectrum.
Document 1
Norio OHTOMO, Kazuo TOKIWANO, Yukio TANAKA, Ayako SUMI, Saburou TERACHI and Hidetoshi KONNO, “Exponential Characteristics of Power Spectral Densities Caused by Chaotic Phenomena,” Journal of the Physical Society of Japan, Vol. 64, No. 4 (1995), pages 1104-1113
Document 2
Supervised by Saichi HOSODA, Edited by Hiroshi KASANUKI and Norio OHTOMO, “New Development of Biological Time Series Data Analysis (in Japanese),” Book Publishing Committee, Hokkaido University, 25 Dec., 1996, pages 139-155
Document 3
Ayako SUMI, “Practice of Biological Time Series Data Analysis by MemCalc (in Japanese),” Published by Nihon Shuhjutsuki Jikan Igaku Kenkyukai (=Japanese Perioperative Research Organization), Mar. 10, 2001
The spectra of electroencephalogram data are exponential spectra and the overall trend of an exponential spectrum varies depending on the state of each subject. Therefore, it can be immediately expected that the value of the gradient can be used as an indicator of the state of the subject.
The inventor developed Makin (trade name) and Makin2 (trade name) as systems for simply obtaining the overall trend of exponential spectra of electroencephalograms in real time, and the systems are used in many research institutes. Therefore, various findings concerning the behavior of gradients are accumulated and reported.
However, presently the state of each subject cannot be identified yet by referring to the value of the gradient only. For example, both the overall trend of the exponential spectrum of the electroencephalogram obtained under anesthesia and the overall trend of the exponential spectrum of the electroencephalogram obtained during sound sleep are sharp, and therefore it is impossible to decide whether a person is anesthetized or is soundly sleeping, by referring to the value of the gradient only. Further, it can sometimes happen that a technician determines that subjects are in the same sleep stage, even though their electroencephalograms are greatly different in gradient. Gradients can also be greatly different from subject to subject. For widely and practically using the remarkable feature that the spectra of electroencephalogram data are exponential, any technical idea for breaking through the present situation as described above is needed.